Решите неравенство: 1/2 x^2-1/2 x-6<0.

\[\frac{1}{2}x^{2} - \frac{1}{2}x - 6 < 0\ \ \ \ | \cdot 2\]

\[x^{2} - x - 12 < 0\]

\[D = ( - 1)^{2} - 4 \cdot 1 \cdot ( - 12) =\]

\[= 1 + 48 = 49\]

\[x_{1} = \frac{1 + \sqrt{49}}{2 \cdot 1} = \frac{1 + 7}{2} = \frac{8}{2} = 4;\ \ \ \ \ \]

\[x_{2} = \frac{1 - \sqrt{49}}{2 \cdot 1} = \frac{1 - 7}{2} = - 3\]

\[Ответ:( - 3;4).\]